President Obama and leaders of both houses of Congress left a 90-minute meeting at the White House this evening no more closer to ending a government shutdown.

Neither side gave any indication that the talks, however cordial, moved them toward a compromise.

"They will not negotiate," House Speaker John Boehner told reporters after leaving the West Wing. "We had a nice conversation, a light conversation, but at some point we've got to allow the process the Congress gave us to work out."

Boehner insists that Democrats in the Senate send negotiators to a conference with House Republicans to work out the differences between the two sides on the budget.

But Democratic leaders Rep. Nancy Pelosi, D-Calif., and Sen. Harry Reid, D-Nev., said the president reiterated that they would hold firm in their position.

"This has never happened before, for a political party to be will willing to take the country to the brink of financial disaster," said Reid, the Senate majority leader. "We're through playing these little games."

Pelosi, House minority leader, warned that the combination of the government shutdown and the threat of a default if Congress fails to raise the debt ceiling by Oct. 17 would be "cataclysmic."

Earlier in the day, President Obama, in an interview with CNBC, said he was "exasperated" by a continued standoff, and warned that financial executives would be wise to be concerned that Congress might fail to raise the debt ceiling.

"When you have a situation in which a faction is willing to potentially default on U.S. government obligations, then we are in trouble," he said.

"And if they're willing to do it now, they'll be willing to do it later."

It also comes as congressional Republicans are increasingly under pressure today to either hold their ground or take an escape hatch offered to them by Democrats and a small but growing number of moderate Republicans who seek to end the unpopular shutdown.

To do so would require the House to abandon its efforts to alter the Affordable Care Act, and instead pass a so-called "clean" funding bill that the Senate and President Obama could accept.

"I'm concerned about those that are on furlough right now," Rep. Michael Grimm, R-N.Y., told ABC News. "I know what it's like to make $30,000 a year and barely be able to pay your rent.

"My heart goes out to those people and that's why I will do whatever I have to do to fund the government, to get this shutdown over."

The strategy, now backed by 17 lawmakers and counting, would likely require that a Republican-led House of Representatives rely principally on Democratic votes and at least 17 Republicans to approve the bill.

But it could further weaken House Speaker John Boehner, R-Ohio, who has had difficulty navigating through the crisis in a way that satisfies the more conservative, tea party-backed wing of his party.

While a "clean" bill would give Boehner a fast way to put a stop to the negative impact a shutdown has on Republicans in public opinion, it would certainly infuriate conservatives in the Republican Party's base, who have lobbied the leaders of their caucus for months to take a stand on this issue.

The political pressure only intensified after Republicans' latest strategy, to ameliorate some of the shutdown's effects on veterans, national parks and the District of Columbia, failed to pass in the House Tuesday night and it faced certain rejection in the Senate and from the White House.

If Boehner chooses to hold his ground, however, there is a growing belief that the shutdown could last for days or weeks.

Already, the White House announced today that Obama canceled his trip to Malaysia and the Philippines scheduled for next week, indicating that the White House believes the shutdown could continue into a second week.

And some Republicans see a political upside in merging negotiations over the funding of the government, with a separate negotiation process over raising the debt ceiling.

If Congress does not vote to raise the debt ceiling by Oct. 17, the country would default on its debts.

President Obama warned Republicans Tuesday against taking this fight to the upcoming debt-ceiling deadline.

"The last time Republicans even threatened this course of action -- many of you remember, back in 2011 -- our economy staggered, our credit rating was downgraded for the first time," Obama said in the Rose Garden Tuesday.

"If they go through with it this time and force the United States to default on its obligations for the first time in history, it would be far more dangerous than a government shutdown, as bad as a shutdown is."